TVR-DART swMATH ID: 27583 Software Authors: Zhuge, Xiaodong; Palenstijn, Willem Jan; Batenburg, Kees Joost Description: TVR-DART: a more robust algorithm for discrete tomography from limited projection data with automated gray value estimation. In this paper, we present a novel iterative reconstruction algorithm for discrete tomography (DT) named total variation regularized discrete algebraic reconstruction technique (TVR-DART) with automated gray value estimation. This algorithm is more robust and automated than the original DART algorithm, and is aimed at imaging of objects consisting of only a few different material compositions, each corresponding to a different gray value in the reconstruction. By exploiting two types of prior knowledge of the scanned object simultaneously, TVR-DART solves the discrete reconstruction problem within an optimization framework inspired by compressive sensing to steer the current reconstruction toward a solution with the specified number of discrete gray values. The gray values and the thresholds are estimated as the reconstruction improves through iterations. Extensive experiments from simulated data, experimental μCT, and electron tomography data sets show that TVR-DART is capable of providing more accurate reconstruction than existing algorithms under noisy conditions from a small number of projection images and/or from a small angular range. Furthermore, the new algorithm requires less effort on parameter tuning compared with the original DART algorithm. With TVR-DART, we aim to provide the tomography society with an easy-to-use and robust algorithm for DT. Homepage: https://ieeexplore.ieee.org/document/7345565 Related Software: ASTRA; UNLocBoX; Matlab; AIR tools; Trace; CoShaRP; RELION; fpylll; GitHub; Unimodularity Test; Unimodularity; PDCO; XDesign; Python; ODL; STIR; tomoRecon; SPGL1; Spot; ASTRA Cited in: 23 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year TVR-DART: a more robust algorithm for discrete tomography from limited projection data with automated gray value estimation. Zbl 1408.94851Zhuge, Xiaodong; Palenstijn, Willem Jan; Batenburg, Kees Joost 2016 all top 5 Cited by 53 Authors 6 Batenburg, Kees Joost 3 Pagani, Silvia M. C. 3 Palenstijn, Willem Jan 3 Sijbers, Jan 3 Tijdeman, Robert 2 Dulio, Paolo 2 Hajdu, Lajos 2 van Aarle, Wim 2 van Leeuwen, Tristan 2 Vanroose, Wim 2 Zhuge, Xiaodong 1 Bleichrodt, Folkert 1 Brunetti, Sara 1 Ceko, Matthew 1 Cools, Siegfried 1 Da, Yihui 1 Dong, Guirong 1 Dong, Yiqiu 1 Fortes, Wagner 1 Ghysels, Pieter 1 Gondzio, Jacek 1 Holman, Sean F. 1 Huthwaite, Peter 1 Jones, Glenn Arthur 1 Kadu, Ajinkya 1 Kojima, Takeshi 1 Lange, Jan-Hendrik 1 Lassas, Matti J. 1 Latva-Äijö, Salla-Maaria 1 Li, Hongwei 1 Liu, Dianzi 1 Lukić, Tibor 1 Nagy, Ábris 1 Németh, József 1 Öktem, Ozan 1 Peri, Carla 1 Pfetsch, Marc E. 1 Qian, Zhenghua 1 Richardson, Philip 1 Ringh, Axel 1 Ruymbeek, Koen 1 Seib, Bianca M. 1 Siltanen, Samuli 1 Tillmann, Andreas M. 1 Ueta, Tetsushi 1 Vincze, Csaba 1 Wang, Bin 1 Wu, Chunlin 1 Xu, Jingqiu 1 Yan, Shi 1 Yoshinaga, Tetsuya 1 Zanetti, Filippo 1 Zhao, Yunsong all top 5 Cited in 9 Serials 5 Discrete Applied Mathematics 5 Inverse Problems 3 Journal of Mathematical Imaging and Vision 2 Journal of Computational and Applied Mathematics 2 IEEE Transactions on Image Processing 1 International Journal of Engineering Science 1 Numerical Algorithms 1 Mathematical Problems in Engineering 1 Inverse Problems in Science and Engineering all top 5 Cited in 17 Fields 10 Information and communication theory, circuits (94-XX) 9 Computer science (68-XX) 7 Biology and other natural sciences (92-XX) 6 Numerical analysis (65-XX) 3 Integral transforms, operational calculus (44-XX) 3 Operations research, mathematical programming (90-XX) 2 Convex and discrete geometry (52-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) Citations by Year